When you parse a sentence, you break it into parts and analyze each element carefully. When your sweetheart shouts "You never listen!" it's a bad idea to parse that by replying, "I just heard you, so I must be listening."
The ability to successfully parse language is important. A binding legal contract, for example, should be read very carefully so you know exactly what's going on. You can also parse things that are more personal. You might exhaustively parse the comments of the guy you have a desperate crush on for any hint that he shares your passionate feelings. The sad truth of the matter? If you have to parse, he probably doesn't love you. Apply your parsing skills elsewhere!